Please show work so I can understand how you came to that answer, thank you Chap
ID: 2785803 • Letter: P
Question
Please show work so I can understand how you came to that answer, thank you
Chapter 5-6: Risk and Return and Asset Allocation 1.Rates of Return 1) Arithmetic average return: In-(ri+r2+r3...+ rn)/n 2) Geometric average return: gn [(1 +r)(1 +r2)(1 +rs)..(1 +rn)]1/h-.1 Example: 4 25% Quarterly return 10% 25% -20% Arithmetic: r4- - Geometric: g4- 3) Effective Annual Rate (EAR) (1+ rate for period)Peniods per year - 1 Example: quarterly return of 3% EAR 2. Sharpe ratio Portfolio risk premium/standard deviation Example: Security A (E(r)-10%; 2.25%) vs. security B (E(r)-12%; 5%) (Assume that the Treasury bill rate = 6%) Sharpe ratioA Sharpe ratioB- 3. Asset allocation between a riskv portfolio and a risk-free asset 1) Construct the risky portfolio using stocks, bonds, etc. 2) Find the optimal risky portfolio P (CAL) 3) Determine wi for the risky portfolio and w2 (1-w) for the risk-free asset Example: 1) You invest your money in a risky portfolio P with an expected rate of return of 15% and a standard deviation of 25% and in a T-bill (risk-free asset) with a rate of return of 5%. What percentages of your money mu risky asset and the risk-free asset, respectively, to form a combined portfolio C with arn expected rate of return of 8%?Explanation / Answer
1.
Arithmetic return = (10% + 25% - 20% + 25%) / 4
= 40% / 4
= 10%.
Arithmetic return is 10%.
2.
Geometric return = [(1 + 10%) × (1 + 25%) × (1 – 20%) × (1 + 25%)] ^ (1 / 4) – 1
= (1.375 ^ 0.25) – 1
= 1.0829 – 1
= 8.29%
Geometric return is 8.29%.
3.
Quarterly rate = 3%
Number of quarter in year = 4
Effective annual rate = [(1 + 3%) ^ 4] – 1
= 1.1255 – 1
= 12.55%
Effective annual rate is 12.55%.